Conductors and CAPM

For a long time I used to wonder why orchestras have conductors. I possibly first noticed the presence of the conductor sometime in the 1990s when Zubin Mehta was in the news. And then I always wondered why this person, who didn’t play anything but stood there waving a stick, needed to exist. Couldn’t the orchestra coordinate itself like rockstars or practitioners of Indian music forms do?

And then i came across this video a year or two back.

And then the computer science training I’d gone through two decades back kicked in – the job of an orchestra conductor is to reduce an O(n^2) problem to an O(n) problem.

For a  group of musicians to make music, they need to coordinate with each other. Yes, they have the staff notation and all that, but still they need to know when to speed up or slow down, when to make what transitions, etc. They may have practiced together but the professional performance needs to be flawless. And so they need to constantly take cues from each other.

When you have $n$ musicians who need to coordinate, you have $\frac{n.(n-1)}{2}$ pairs of people who need to coordinate. When $n$ is small, this is trivial, and so you see that small ensembles or rock bands can easily coordinate. However, as $n$ gets large, $n^2$ grows well-at-a-faster-rate. And that is a problem, and a risk.

Enter the conductor. Rather than taking cues from one another, the musicians now simply need to take cues from this one person. And so there are now only $n$ pairs that need to coordinate – each musician in the band with the conductor. Or an $O(n^2)$ problem has become an $O(n)$ problem!

For whatever reason, while I was thinking about this yesterday, I got reminded of legendary finance professor R Vaidya‘s class on capital asset pricing model (CAPM), or as he put it “Sharpe single index model” (surprisingly all the links I find for this are from Indian test prep sites, so not linking).

We had just learnt portfolio theory, and how using the expected returns, variances and correlations between a set of securities we could construct an “efficient frontier” of securities that could give us the best risk-adjusted return. Seemed very mathematically elegant, except that in case you needed to construct a portfolio of $n$ stocks, you needed $n^2$ correlations. In other word, an $O(n^2)$ problem.

And then Vaidya introduced CAPM, which magically reduced the problem to an $O(n)$ problem. By suddenly introducing the concept of an index, all that mattered for each stock now was its beta – the coefficient of its returns proportional to the index returns. You didn’t need to care about how stocks reacted with each other any more – all you needed was the relationship with the index.

In a sense, if you think about it, the index in CAPM is like the conductor of an orchestra. If only all $O(n^2)$ problems could be reduced to $O(n)$ problems this elegantly!

Gults and Grammar

Back in IIT, it was common to make fun of people from Andhra Pradesh for their poor command over the English language. It was a consequence of the fact that JEE coaching is far more institutionalised in that (undivided) state, because of which people come to IIT from less privileged backgrounds (on average) than their counterparts in Karnataka or Tamil Nadu or Maharashtra.

Now, in hindsight, making fun of people’s English doesn’t sound particularly nice, but sometimes stories come up that make it incredibly hard to resist.

This one is from Matt Levine’s newsletter. And it is about an insider trading ring. This is a quote that Levine has quoted in his newsletter (pay attention to the names):

According to the SEC’s complaint, Janardhan Nellore, a former IT administrator then at Palo Alto Networks Inc., was at the center of the trading ring, using his IT credentials and work contacts to obtain highly confidential information about his employer’s quarterly earnings and financial performance. As alleged in the complaint, until he was terminated earlier this year, Nellore traded Palo Alto Networks securities based on the confidential information or tipped his friends, Sivannarayana Barama, Ganapathi Kunadharaju, Saber Hussain, and Prasad Malempati, who also traded.

The SEC’s complaint alleges that the defendants sought to evade detection, with Nellore insisting that the ring use the code word “baby” in texts and emails to refer to his employer’s stock, and advising they “exit baby,” or “enter few baby.” The complaint also alleges that certain traders kicked back trading profits to Nellore in small cash transactions intended to avoid bank scrutiny and reporting requirements. After the FBI interviewed Nellore about the trading in May, he purchased one-way tickets to India for himself and his family and was arrested at the airport.

You can look at Levine’s newsletter to understand his take on the story (it’s towards the bottom), but what catches my eye is the grammar. I think it is all fine to refer to the insider-traded stock as a “baby”, but at least be grammatically correct about it!

“Enter few baby” is so obviously grammatically incorrect (it’s hard to even be a typo) that when intercepted by someone like the SEC, it would immediately send alarm bells ringing. Which is what I suppose possibly happened.

So my take on this case is – don’t insider  trade, but even if you do, be grammatical about your signals. If you’re so obviously grammatically wrong, it is easy for whoever intercepts your chats to know you’re up to something fishy.

But then if you’re gult..

Volatility and price differentiation

In a rather surreal interview to the rather fantastically named Aurangzeb Naqshbandi and Hindustan Times editor Sukumar Ranganathan, Congress president Rahul Gandhi has made a stunning statement in the context of agricultural markets:

Markets are far more volatile in terms of rapid price differentiation, than they were before.

I find this sentence rather surreal, in that I don’t really know what Gandhi is talking about. As a markets guy and a quant, there is only one way in which I interpret this statement.

It is about how market volatility is calculated. While it might be standard to use standard deviation as a measure of market volatility, quants prefer to use a method called “quadratic variation” (when the market price movement follows a random walk, quadratic variation equals the variance).

To calculate quadratic variation, you take market returns at a succession of very small intervals, square these returns and then sum them up. And thinking about it mathematically, calculating returns at short time intervals is similar to taking the derivative of the price, and you can call it “price differentiation”.

So when Gandhi says “markets are far more volatile in terms of rapid price differentiation”, he is basically quoting the formula for quadratic variation – when the derivative of the price time series goes up, the market volatility increases by definition.

This is what you have, ladies and gentlemen – the president of the principal opposition party in India has quoted the formula that quants use for market volatility in an interview with a popular newspaper! Yet, some people continue to call him “pappu”.

Suckers still exist

1. You give Citigroup Inc. $1,000, when Amazon.com’s stock is at$1,339.60.
2. At the end of each quarter for the next three years, Citi looks at Amazon’s stock price. If it’s at or below $1,339.60, Citi sends you$25 and the trade continues. If it’s above $1,339.60, Citi sends you back your$1,000 and the trade is over.
3. At the end of the three years, Citi looks at Amazon’s stock price. If it’s above $1,004.70 (75 percent of the initial stock price), then Citi sends you$1,025 and the trade is over. But if it’s below $1,004.70, you eat the full amount of the loss: For instance, if Amazon’s stock price is$803.80 (60 percent of the initial stock price), then you lose 40 percent of your money, and get back only $600. Citi keeps the rest. (You get to keep all the premiums, though.) Anyone with half a brain should know that this is not a great trade. For starters, it gives the client (usually a hedge fund or a pension fund or someone who represents rich guys) a small limited upside (of 10% per year for three years), while giving unlimited downside if Amazon lost over 25% in 3 years. Then, the trade has a “knock out” (gets unwound with Citigroup paying back the client the principal) clause, with the strike price of the knockout being exactly the Amazon share price on the day the contract came into force. And given that Amazon has been on a strong bull run for a while now, it seems like a strange price at which to put a knock out clause. In other words, there is a high probability that the trade gets “knocked out” soon after it comes into existence, with the client having paid up all the transaction costs (3.5% of the principal in fees). Despite this being such a shitty deal, Levine reports that Citigroup sold$16.3 million worth of these “notes”. While that is not a large amount, it is significant that nearly ten years after the financial crisis, there are still suckers out there, whom clever salespersons in investment banks can con into buying such shitty notes. It seems institutional memory is short (or these clients are located in states in the US where marijuana is legal).

PS: Speaking of suckers, I recently got to know of the existence of a school in Mumbai named “Our Lady of Perpetual Succour“. Splendid.

Indexing, Communism, Capitalism and Equilibrium

Leading global research and brokerage firm Sanford Bernstein, in a recent analyst report, described Index Funds (which celebrated their 40th birthday yesterday) as being “worse than Marxism“. This comes on the back of some recent research which have accused index funds of fostering “anticompetitive practices“.

According to an article that says that indexing is “capitalism at its best“, Sanford Bernstein’s contention is that indexers “free ride” on the investment and asset allocation decisions made by active investors who spend considerable time, money and effort in analysing the companies in order to pick the best stocks.

Sanford Bernstein, in their report, raise the spectre of all investors abandoning active stock picking and moving towards index funds. In this world, they argue, allocations to different assets will not change (since all funds will converge on a particular allocation), and there will be nobody to perform the function of actually allocating capital to companies that deserve them. This situation, they claim, is “worse than Marxism”.

The point, however, is that as long as there is no regulation that requires everyone to move to index funds, this kind of an equilibrium can never be reached. The simple fact of the matter is that as more and more people move to indexing, the value that can be gained from fairly basic analysis and stock picking will increase. So there will always be a non-negative flow (even if it’s a trickle) in the opposite direction.

In that sense, there is an optimal “mixed strategy” that the universe of investors can play between indexing and active management (depending upon each person’s beliefs and risk preferences). As more and more investors move to indexing, the returns from active management improve, and this “negative feedback” keeps the market in equilibrium!

So in that sense, it doesn’t matter if indexing is capitalist or communist or whateverist. The negative feedback and varying investor preferences means that there will always be takers for both indexing and active management. Whether we are already at equilibrium is another question!

Continuous and barrier regulation

One of the most important pieces of financial regulation in the US and Europe following the 2008 financial crisis is the designation of certain large institutions as “systemically important”, or in other words “too big to fail”. Institutions thus designated have greater regulatory and capital requirements, thus rendering them at a disadvantage compared to smaller competitors.

This is by design – one of the intentions of the “SiFi” (systemically important financial regulations) is to provide incentives to companies to become smaller so that the systemic risk is reduced. American insurer Metlife, for example, decided to hive off certain divisions so that it’s not a SiFi any more.

AIG, another major American insurer (which had to be bailed out during the 2008 financial crisis), is under pressure from its activist investors led by Carl Icahn to similarly break up so that it can avoid being a SiFi. The FT reports that there were celebrations in Italy when insurer Generali managed to get itself off the global SiFi list. Based on all this, the SiFi regulation seems to be working in spirit.

The problem, however, is with the method in which companies are designated SiFis, or rather, with that SiFi is a binary definition. A company is either a SiFi or it isn’t –  there is no continuum. This can lead to perverse incentives for companies to escape the SiFi tag, which might undermine the regulation.

Let’s say that the minimum market capitalisation for a company to be defined a SiFi is $10 billion (pulling this number out of thin air, and assuming that market cap is the only consideration for an entity to be classified as a SiFi). Does this mean that a company that is worth$10 Bn is “systemically important” but one that is worth $9.9 Bn is not? This might lead to regulatory arbitrage that might lead to a revision of the benchmark, but it still remains a binary thing. A better method for regulation would be for the definition of SiFi to be continuous, or fuzzy, so that as the company’s size increases, its “SiFiness” also increases proportionally, and the amount of additional regulations it has to face goes up “continuously” rather than being hit by a “barrier”. This way, the chances of regulatory arbitrage remain small, and the regulation will indeed serve its purpose. SiFi is just one example – there are several other cases which are much better served by regulating companies (or individuals) as a continuum and not classifying them into discrete buckets. When you regulate companies as parts of discrete buckets, there is always the temptation to change just enough to move from one bucket to the other, and that might result in gaming. Continuous regulation, on the other hand, leaves no room for such marginal gaming – marginal changes aer only giong to have a marginal impact. Perhaps for something like SiFi, where the requirements of being a SiFi are binary (compliance, etc.) there may not be a choice but to keep the definition discrete (if there are 10 different compliance measures, they can kick in at 10 different points, to simulate a continuous definition). However, when the classification results in monetary benefits or costs (let’s say something like SiFis paying additional regulatory costs) it can be managed via non-linear funding. Let’s say that you pay 10% fees (for whatever) in category A and 12% in category B (which you get to once you cross a benchmark). A simply way to regulate would be to have the fees as a superlinear function of your market cap (if that’s what the benchmark is based on). Ladder Theory and Local Optima According to the Ladder Theory, women have two “ladders”. One is the “good ladder” where they rank and place men they want to fuck. The rest of the men get placed on the “friends ladder”. Men on the other hand have only one ladder (though I beg to disagree). The question is what your strategy should be if you end up on top of the “wrong” (friends) ladder. On the one hand, you get your “dove“‘s attention and mostly get treated well there. On the other hand, that’s not where you intended to end up. Far too many people at the top of the friends ladder remain there because they are not bold enough to take a leap. They think it is possible to remain there (so that they “preserve the friendship”) and at the same time make their way into the dove’s good ladder. Aside 1: The reason they want to hold on to their friendship (though that’s not the reason they got close to the dove) can be explained by “loss aversion” – having got the friendship, they are loathe to let go of it. This leads them to pursuing a risk-free strategy, which is unlikely to give them a big upside. Aside 2: A popular heuristic in artificial intelligence is Hill Climbing , in which you constantly take the path of maximum gradient. It can occasionally take you to the global maximum, but more often than not leaves you at a “local maximum”. Improvements on hill climbing (such as Simulated Annealing) all involve occasionally taking a step down in search of higher optimum. Behavioural economics and computer science aside, the best way to analyse the situation when you’re on top of the friends ladder is using finance. Financial theory tells you that it is impossible to get a large risk-free upside (for if you could, enough people would buy that security that the upside won’t be significant any more). People on top of the friends ladder who want to preserve their friendships while “going for it” are delusional – they want the risk-free returns of the friendship at the same time as the possibility of the grand upside of getting to the right ladder. They should understand that such trades are impossible. They should also understand that they might be putting too high a price on the friendship thanks to “loss aversion”, and that the only way to escape the current “local optimum” is by risking a downward move. They should remember that the reason they got close to their dove was NOT that they end up on the friends ladder, and should make the leap (stretching the metaphor). They might end up between two stools (or ladders in this case), but that might be a risk well worth taking! PS: this post is not a result of my efforts alone. My Wife, who is a Marriage Broker Auntie, contributed more than her share of fundaes to this, but since she’s too lazy to write, I’m doing the honours. Revenue management in real estate Despite there continuing to be large amounts of unsold inventory of real estate in India, prices refuse to drop. The story goes that the builders are hoping to hold on to the properties till the prices rebound again, rather than settling for a lower amount. While it is true that a number of builders are stressed under bank loans since banks have pretty much stopped financing builders, this phenomenon of holding on to houses while waiting for prices to recover is actually a fair strategy, and a case of good revenue management. Let me illustrate using my building. There are eight units in my building which was built as a joint venture between the erstwhile owner of the land on which the building stands and the builder, both receiving four units each. The builder, on his part, sold one unit from his share very soon after construction began. Given the total costs of construction, the money raised from sale of that one apartment went a long way in funding the construction of the building. It wasn’t fully enough – the builder faced some cash flow issues thanks to which construction got delayed, but since he managed to raise that cash, he didn’t need to sell any other units belonging to his share. He continues to own his other three units (and has rented out all of them). The economics of real estate in India are such that the cost of land forms a significant part of the cost of an apartment. According to a lawyer I had spoken to during the purchase of my property (he also has interests in the construction industry), builders see a significant (>100%) profit margin (not accounting for cost of capital) in projects such as my building. What this implies is that once the builder has taken care of the cost of land (by paying for it in terms of equity, for example, like in the case of my building), all he needs to do to fund the cost of construction is to sell a small fraction of the units. And once these are sold, there is absolutely no urgency to sell the rest. Hence, as long as the builder expects prices to recover (when it comes to house prices, builders are usually an optimistic lot), he would rather wait it out (when he can realise a higher price) than sell it currently at depressed prices. Hence, downturns in housing markets are not characterised by an actual drop in prices (few builders are willing to drop prices) but by a drop in the volume of transactions. While there might be a large number of housing units that remain unsold, it is unlikely that there are apartment complexes which are completely unsold – there will be a handful of bargain-hunting early buyers who would have bought and funded the construction of the complex. And given the low occupancy rates, these people are losers in the deal, for it will be hard for them to move in. And it is also rational for the builder to invest in new projects even when they are currently holding on to significant inventory. All they need to do is to find a willing partner who can contribute the necessary real estate in the form of equity. And new projects will inevitably find the first set of early buyers looking for a bargain, irrespective of the builder’s track record. And so the juggernaut rolls on.. Finance is boring, once again So IIMB goes to placements this week. Two months back, though, in the first class I taught there, in an attempt to “understand the class”, I asked my students to tell me their “most preferred employer”. The intention was to tailor the course in a way that would be more suitable for their prospective careers. Thinking back at that class, there is one thing that hits me – very few want to do finance (again that’s no indication of how many of them will end up in finance jobs this week). I initially thought it was a biased sample – there was a course of the same name offered to the same batch in an earlier term, and those that had taken the course then were not eligible to take the course now. Given the primacy of spreadsheets in finance, I thought students more inclined towards finance would have taken the course in the earlier offering. But then thinking about it (without data to back me), that so few want to do finance doesn’t surprise me at all. When I tried putting myself in the shoes of my students and thought of what jobs I wanted to take, I realised that there weren’t any finance jobs that I could think of. With the derivatives world having undergone several downturns in the last decade, no one recruits for derivative sales and trading from IIMs any more (if my information sources are right – they could be wrong). And if you were to take out derivatives sales and trading, there is very little that excites about the other finance jobs that recruit MBAs. There is investment banking (M&A, Equity/Debt Capital Markets) of course, but the job is insanely fighter, and while it is ultimately a finance job, finance forms a small portion of your day-to-day activities there (secondhand information again). Venture capital and private equity are again ostensibly finance but again there is very little finance you use in decision-making there – other “softer” stuff (such as evaluating “quality of founding team”, etc.) dominate. Then there is commercial banking, which is finance only in name, for most jobs for which they recruit MBAs (data from a decade back) are in the realm of sales or business development. There is the odd treasury or risk management job, but those jobs are small in number compared to the others. And corporate finance jobs see excitement very rarely (when there is M&A or related activity). You have asset management and research roles, but they are again not the kind that you would call as “exciting”. In short, finance has become boring, again. Most jobs on offer to fresh MBAs nowadays are for roles that are fairly routine and “boring” for the most part, and while finance still pays well, there are no adrenaline-pumping jobs on offer there as there used to be a decade ago. And from the macro point of view, that is a good thing. Because finance is fundamentally a boring job, and is supposed to be a boring job. If finance had become “exciting”, it was because finance people were doing stuff that they were not supposed to be doing! Like taking highly levered bets for example, or concocting derivatives so complicated that nobody – not even most traders – would be able to understand it. I had written recently that people have stopped considering coding “cool”, and that we should do something about it. A similar thing is happening to finance, where MBA students are not finding it “cool” any more (but people will take up the profession since it pays well). However, this is not a problem, and nothing needs to be done about it. This is how things ought to be. Finance is supposed to be boring! Anyway, this might be biased opinion since if I could roll back nine years and were asked to pick a job, I couldn’t see myself working at ANY of the companies that had come to recruit from IIMB back when I graduated! So perhaps my hypothesis about finance jobs being boring now is a result of all typical post-MBA jobs being boring! Perhaps that explains why I’m doing what I’m doing now – a “job” so atypical it takes a lot of effort to explain to people what I’m doing. Oh, and coming back to finance, I’m four weeks though with my Asset Pricing MOOC, and have been totally enjoying it so far! A misspent career in finance I spent three years doing finance – not counting any internships or consulting assignments. Between 2008 and 2009 I worked for one of India’s first High Frequency Trading firms. I worked as a quant, designing intra-day trading strategies based primarily on statistical arbitrage. Then in 2009, I got an opportunity to work for the big daddy of them all in finance – the Giant Squid. Again I worked as a quant, designing strategies for selling off large blocks of shares, among others. I learnt a lot in my first year there, and for the first time I worked with a bunch of super-smart people. Had a lot of fun, went to New York, played around with data, figured that being good at math wasn’t the same as being good at data – which led me to my current “venture”. But looking back, I think I mis-spent my career in finance. While quant is kinda sexy, and lets you do lots of cool stuff, I wasn’t anywhere close to the coolest stuff that my employers were doing. Check out this, for example, written by Matt Levine in relation to some tapes regarding Goldman Sachs and the Fed that were published yesterday: The thing is: • Before this deal, Santander had received cash (from Qatar), and agreed to sell common shares (to Qatar), but wasn’t getting capital credit from its regulators. • After this deal, Santander had received cash (from Qatar), and agreed to sell common shares (to Qatar), and was getting capital credit from its regulators, and Goldman was floating around vaguely getting$40 million.

This is such brilliantly devious stuff. Essentially, every bad piece of regulation leads to a genius trade. You had Basel 2 that had lesser capital requirements for holding AAA bonds rather than holding mortgages, so banks had mortgages converted into Mortgage Backed Securities, a lot of which was rated AAA. In the 1980s, there were limits on how much the World Bank could borrow in Switzerland and Germany, but none on how much it could borrow in the United States. So it borrowed in the United States (at an astronomical interest rate – it was the era of Paul Volcker, remember) and promptly swapped out the loan with IBM, creating the concept of the interest rate swap in that period.

In fact, apart form the ATM (which Volcker famously termed as the last financial innovation that was useful to mankind, or something), most financial innovations that you have seen in the last few decades would have come about as a result of some stupid regulation somewhere.

Reading articles such as this one (the one by Levine quoted above) wants me to get back to finance. To get back to finance and work for one of the big boys there. And to be able to design these brilliantly devious trades that smack stupid regulations in the arse! Or maybe I should find myself a job as some kind of a “codebreaker” in a regulatory organisation where I try and find opportunities for arbitrage in any potentially stupid rules that they design (disclosure: I just finished reading Cryptonomicon).

Looking back, while my three years in finance taught me much, and have put me on course for my current career, I think I didn’t do the kind of finance that would give me the most kick. Maybe I’m not too old and I should give it another shot? I won’t rule that one out!

PS: back when I worked for the Giant Squid, a bond trader from Bombay had come down to give a talk. I asked him a question about regulatory arbitrage. He didn’t seem to know what that meant. At that point in time I lost all respect for him.